1. No category

G.CO.5 WORKSHEET #10
NAME: ______________________
1
1. Determine whether the double reflection over lines m and n produce a Translation or a Rotation.
(Lines that appear to be parallel are parallel.)
E
a)
b)
c)
d)
E
m
E
m
D
n
D
F 41°
D
F
n
D
m
F
F
74°
n
Translation / Rotation
Translation / Rotation
Translation / Rotation
n
m
Translation / Rotation
2. Determine the distance and direction of these double reflections over parallel lines.
(Lines that appear to be horizontal or vertical are.)
a)
b)
c)
n
E
E
6 units
n
4 units
m
n
E
m
D
E
D
F
F
D
7.5 units
m
F
Rn Rm (∆DEF )
Rn Rm (∆DEF )
Rm Rn (∆DEF )
Distance of Translation ________
Distance of Translation ________
Distance of Translation ________
Direction
Direction
Direction
UP DOWN RIGHT LEFT
UP DOWN RIGHT LEFT
UP DOWN RIGHT LEFT
d)
e)
D
E
f)
n
0.75 units
m
F
n
m
F
D
E
Rn Rm (∆DEF )
Rn Rm (∆DEF )
Rn Rm (∆DEF )
Distance of Translation ________
Distance of Translation ________
Distance of Translation ________
Direction
Direction
Direction
UP DOWN RIGHT LEFT
UP DOWN RIGHT LEFT
UP DOWN RIGHT LEFT
3. If m || n, then would
n
m
D
F
n
F
e
E
m
D
E
11 units
3 units
5 units
Rn Rm (∆DEF ) produce a translation? Explain.
G.CO.5 WORKSHEET #10
2
4. Circle the correct answers.
a) R y = 4 R y = 2 ( ∆ABC ) would result in a translation to the right / left / up / down a total of 2 / 4 / 8 units
b) Ry = −1 Ry = 5 (∆ABC ) would result in a translation to the right / left / up / down a total of 4 / 6 / 12 units
c) Rx = 1 Rx = − 4 ( ∆ABC ) would result in a translation to the right / left / up / down a total of 5 / 10 / 12 units
d) Rx = 1 Rx = 2 ( ∆ABC ) would result in a translation to the
right / left / up / down a total of 1 / 2 / 4 units
5. Determine the resultant rotation angle value from the double reflection over intersecting lines.
(More than one answer is possible for each of these question – we will use acute angle to determine the rotation value.)
a)
b)
n
D
c)
n
E
46°
71°
m
D
E
F
D
m
18°
F
m
E
n
F
Rn Rm (∆DEF )
Rn Rm (∆DEF )
Rm Rn (∆DEF )
Resultant Rotation
Angle Value
Resultant Rotation
Angle Value
Resultant Rotation
Angle Value
____________
____________
____________
d)
e)
F
f)
n
n
E
n
D
20°
30°
k
m
64°
E
F
E
D
m
m
D
F
Rm Rn (∆DEF )
Rn Rm (∆DEF )
Rm Rn (∆DEF )
Resultant Rotation
Angle Value
Resultant Rotation
Angle Value
Resultant Rotation
Angle Value
____________
____________
____________
6. Could an odd number of reflections ever be a translation? Why or why not?
G.CO.5 WORKSHEET #10
3
7. Could a reflection followed by a rotation ever be described as a single rotation?
8. If you Rx = 4 Rx = 2 ( ∆ABC ) you would get a translation of A to A’’ to the right 4 units. What would happen if
you had done Rx = 4 Rx = 2 Rx = 4 Rx = 2 ( ∆ABC ) ?
9. Determine the resultant translation direction.
a) R y = 4 Ry = − 2 ( P)
translates all points
up / down / right / left
b) R y = − 2 Ry = 4 ( P)
translates all points
up / down / right / left
c) Rx = 3 Rx = 5 ( P )
translates all points
up / down / right / left
d) Rx = 5 Rx = 3 ( P )
translates all points
up / down / right / left
10. Complete the following – Convert the double reflection over parallel lines into a single translation.
a)
Ry = 3 Ry = −1 ( x, y ) = T〈 _____,_____ 〉 ( x, y)
b)
Ry = −5 Ry = 2 ( x, y ) = T〈 _____,_____ 〉 ( x, y )
c)
Rx = −3 Rx = 0 ( x, y) = T〈 _____,_____ 〉 ( x, y)
d)
Rx = 6 Rx = 4 ( x, y ) = T〈 _____,_____ 〉 ( x, y )
e)
Ry = 1 Ry = −1 ( x, y) = T〈 _____,_____ 〉 ( x, y)
f)
Rx = 1 Rx = − 2 ( x, y ) = T〈 _____,_____ 〉 ( x, y )
11. Complete the following – Convert the double reflection over intersecting lines into a single rotation.
a)
Ry axis Rx axis ( x, y) = RO, _______ ( x, y)
b)
Ry axis Rx axis ( x, y ) = RO, _______ ( x, y )
c)
Ry axis Ry = x ( x, y ) = RO, _______ ( x, y)
d)
Rx axis Ry = x ( x, y) = RO, _______ ( x, y)
e)
Ry = x Ry axis ( x, y ) = RO, _______ ( x, y )
f)
Ry = x Rx axis ( x, y ) = RO, _______ ( x, y )
G.CO.5 WORKSHEET #10
4
12. Record the equivalent Rotation for the given Double Reflections over intersecting lines.
______ 1. Ry axis Rx axis
A. RO , 90°
______ 2. Ry = x Rx axis
B. RO , 180°
______ 3. Rx axis Ry = x
C. RO, 270°
______ 4. Ry = x Ry axis
______ 5. Ry axis Ry = x
13. Why would 5 reflections in a NEVER result in a rotation?
14. A student says “To do rotations and translations all we need to really know is reflections.” What does this
student mean by this statement?
15. Two lines m and n intersect each other forming an angle of 76°. Students are asked perform Rm Rn (∆DEF ) .
What are two possible answers for the resultant angle of rotation? Explain.
E
m
D
F
n
76°
G.CO.s WORKSHEET #70
NAME:
d%
1. Determine whether the double reflection over lines m and n produce a Translation*or a Rotation.
to be parallel are parallel.)
(Lines that appear
a)
Translation
/
Rotation
ffiliJil;n/
Rotation
\-=-------'l
2. Determine the distance and direction of these double reflections over parallel lines.
(Lines that appear to be horizontal or vertical are.)
a)
,A
b)
e units I
effi
,Y
\"
{w
m!
R*( DEF)
\"
Distance of Translation
Distance of Translatio
Direction
UP DOWN
RIGHT
uP DowN
LEFT
Distance of Translation
Direction
UP DOWN
Distance of Translation
Direction
RrGHr
6*l)
v
UP DOWN
RIGHT
f)
I
m
J
O-75
units -
rW,
RIGH
11
\"
R*(ADEF)
Distance of Translation
Direction
\
Distance of
"
R^(LDEF)
/
Translation Q
Direction
UP DOWN RIGHT LEFT
3. lf m | | n, then would R," R^(LDEF) produce a transtation?
,w,
\(LDEF)
m
R," R^(LDEF)
m
lL
"
e)
11 units
n
R*"
Direction
,w,
d)
R*(LDEF)
Explain.
uP DowN(Llgi
-_,-u
LEFr
G.CO,s WORKSHEET #10
4. Circle the correct answers.
a) Rr=+" Ry=2(MBC) would result in a translation to the right/ rcft
b) &=-, " R,='(MBC) would result in a translation to the
@tdown
atotal
ot Z t@8
units
right/left/up/down
atotal
of 4 t6t
l2unrts
c) &=, "R,=-:(M,BC) wouldresultinatranslationtothe
q@tteftlup/down
atotal
of s t@l2units
d) &=, "R,-2(MBC) wouldresultinatranslationtothe
right/left/up/down
atotal
of I t 2 I
4units
5. Determine the resultant rotation angle value from the double reflection over intersecting tines.
(More than one answer is possible for each of these question we will use acute angle to determine
the rotation value.)
a)
b)
&" R*(LDEF)
R"" R-(LDEF)
R*" R"(LDEF)
Resultant Rotation
Resultant Rotation
Angle Value
Resultant Rotation
Angle Value
qL"
d)
,
Angle Value
-5b"
e)
f)
64"
R_. R^(LDEF)
\"
Resultant Rotation
Resultant Rotation
Angle Value
Resultant Rotation
Angle Value
Angle Value
R.(LDEF)
t7t'
5. could
an odd number of reflections ever be a translation?
why or why not?
R_. R"(ADEF)
3
G.CO.s WORKSHEET #70
7. Could a reflection followed by a rotation ever be described as a single rotation?
R,=,(MBC) you would get a translation of A to A" to the right 4 units. What would happen if
you had done ,R,=o o&=, o &=o " R,=,(MBC)?
8. ff you &=n
o
\a-" --)/
9. Determine the resultant translation direction.
10. Complete the following
a) Ry=3
c)
-
a) Rr=+" Rr=_r(P)
translates all points
up/down/right/left
b) Rr=_z.l?r=o(P)
translates all points
up
/@/
c) R,=,
'&=r(P)
translates all points
up
/
d) R,=, "R,=,(P)
translates all points
up
/ down l@
11-.
o& --r(x,Y) = T,,_,_r(x,!)
"& =-r(*,y) = T,,-_r(x,!)
Complete the following
-
o
Ry
.) R, =,
o
& **(x, !)
=
*(x, Y)
rieht
I
b)
&=-s "& =r(*,y) = T< O .-l'lr(x,!)
d)
&=o o& =o(x,y) =
Tr_!- o ,(x,!)
fl &=, o& =-r(*,y) = T< (o_ o
,(x,!)
Convert the double reflection over intersecting lines into a single rotation.
,l &*i, o& *x(x,Y) = Ro
.) R, *i,
/
/ teft
Convert the double reflection over parallel lines into a single translation.
&=-: o&=o(r, y) = Tr--r(x,!)
e) Ry=r
down
right
(*, y)
u) Ry
**
o
R,
**(*, Y) = Ro lko
= Ro,-@'Y)
d)
R*
*i, o & = -(*, y) =
* Ro,
a
&
=,
@rY)
o lR,
*ir(x, Y)
fto,
(x,
y)
* Io" (*, y)
= Ro, 40" @, Y)
left
left
G.CO.SWORKSHEfr#70
r
12. Record the equivalent Rotation for the given Double Reflections over intersecting,lines..
L. Rr*xo&*,r
A'4.*'
h z. Ry=*o R**i,
B'fir,,r0"
3. ftr*o oXr=,
c' Ro.z7o"
C 4. Ry=roRrun
5. Rr**o Rr=,
13. Why would 5 reflections in a NEVER result in a rotation?
14. A student says 'To do rotations and translations all we need to really know is reflections."- What does this
student mean by this statement?
I
rne{taa$
ov..-s
v"-4\z#
>*+
od*lv
erru
t\
l,'r*S
--
-h^*^S 1...-{.,ts*-:
{
r-o
i-"r-l
*r.*ia^--
-7
15. Two lines m and n intersect each othei forming an angle of 760. Stucjents are asked perform R-"
What are two possible answers for the resultant angle of rotation? Explain.
\(A,DEF)